Sure, let's work through these conversions step by step.
### Converting [tex]\( 9.25 \times 10^3 \)[/tex] to standard form:
1. Identify the Base Number:
The base number given is [tex]\( 9.25 \)[/tex].
2. Identify the Exponent:
The exponent given is [tex]\( 3 \)[/tex].
3. Understand What [tex]\( 10^3 \)[/tex] Means:
[tex]\( 10^3 \)[/tex] means [tex]\( 10 \)[/tex] raised to the power of [tex]\( 3 \)[/tex], which is [tex]\( 10 \times 10 \times 10 \)[/tex].
4. Multiply the Base Number by [tex]\( 10^3 \)[/tex]:
When you multiply [tex]\( 9.25 \)[/tex] by [tex]\( 10^3 \)[/tex], it shifts the decimal point 3 places to the right.
So, [tex]\( 9.25 \times 10^3 \)[/tex]:
- Shifting 9.25 three places to the right, we get [tex]\( 9250.0 \)[/tex].
Hence, [tex]\( 9.25 \times 10^3 = 9250.0 \)[/tex].
### Converting [tex]\( 27 \times 10^4 \)[/tex] to standard form:
1. Identify the Base Number:
The base number given is [tex]\( 27 \)[/tex].
2. Identify the Exponent:
The exponent given is [tex]\( 4 \)[/tex].
3. Understand What [tex]\( 10^4 \)[/tex] Means:
[tex]\( 10^4 \)[/tex] means [tex]\( 10 \)[/tex] raised to the power of [tex]\( 4 \)[/tex], which is [tex]\( 10 \times 10 \times 10 \times 10 \)[/tex].
4. Multiply the Base Number by [tex]\( 10^4 \)[/tex]:
When you multiply [tex]\( 27 \)[/tex] by [tex]\( 10^4 \)[/tex], it shifts the decimal point 4 places to the right.
So, [tex]\( 27 \times 10^4 \)[/tex]:
- Shifting 27 four places to the right, we get [tex]\( 270000 \)[/tex].
Hence, [tex]\( 27 \times 10^4 = 270000 \)[/tex].
In conclusion:
[tex]\[ 9.25 \times 10^3 = 9250.0 \][/tex]
[tex]\[ 27 \times 10^4 = 270000 \][/tex]
